Sleep disorders often manifest in disruptions to the sleep-wake cycle, making this a critical area of study. Mice, sharing key characteristics with the human sleep-wake cycle, serve as an invaluable model in sleep research. Manual scoring is time-consuming and complicated. The automation of this process is essential. We propose to apply our model-free time series segmentation methods to identify sleep stages. This approach is based on the theory of the \(\epsilon \) -complexity and change-point detection algorithm. After that, the k-means clustering is used to identify the sleep cycles. We applied this method to a set of publicly available mouse EEGs with by-hand sleep scores, which resulted in an overall accuracy rate of about \(89\%\) . Our approach provides an efficient and reliable alternative to manual classification methods in sleep research.